The Astros had a season-high 18 hits and climbed back into a tie for first place with St. Louis in the National League Central Division.
Kent got the Astros going with an RBI double in the first inning, then single in a run in the third for a 3-0 cushion. He capped his big night in the ninth with his first grand slam since Aug. 9, 2000.
Staked to an early lead, Miller (12-11) won for the fifth time in six decisions, taking a shutout into the seventh before allowing a solo homer to Alex Cora.
One day after celebrating his 35th birthday, Dodgers starter Hideo Nomo (15-11) was tagged for four runs and nine hits in five innings.